Are whole numbers polynomials?

A number system is the representation of numbers by using digits or symbols. The representation is made in a consistent manner. The value of the digit in any number can be known by a digit’s position held in the number and the base in which the number system is represented. The representation of the number is done uniquely and arithmetic operations like addition, subtraction, and division are performed on it. 

Types of Number Systems  

The number systems can be classified into different categories, depending on the difference in the base number used to the representation of the number. For instance, we have, 

• Binary number system, which can be represented by base 2.
• Octal number system, which can be represented by base 8. 
• Decimal number system, which can be represented by base 10.
• Hexadecimal number system, which can be represented by base 16.  

What is Polynomial?

A polynomial is composed of two terms, known as Poly, which means “many” and Nominal which mean “terms”. A polynomial can be termed as the expression composed of variables, constants, and exponents. The various elements of the polynomial are combined using mathematical operations such as addition, subtraction, multiplication, and division. 

Types of Polynomials

The polynomials can be classified into different types depending on the difference in the number of terms contained, being, monomial, binomial and trinomial. 

What are Whole Numbers?

The resultant set formed by the set of natural numbers added with the integer 0, forms the whole number set. For instance, 0,1,2,3,4,…∞ comprise the whole number set. 

The smallest whole number is 0. The whole number forms the basic set of numbers. Every whole number is associated with an immediate predecessor that is the number that comes before a whole number. The exception to this property is the whole number 0. Similarly, every whole number has an immediate successor. The whole numbers form a basic part of the set of real numbers, including, integers, rational numbers among others.

Note:

• Natural Numbers are a complete subset of the Whole Numbers.
• Whole Numbers comprise of all the counting numbers.
• Whole Numbers are Real Numbers.
• All positive integers including zero are whole numbers.

Are whole numbers polynomials?

Answer:

Whole numbers contain numerical values. Since, we know, that anything raised to the power of 0 is 1. Therefore, every whole number can be represented in the polynomial form, each of which contains one term. The whole number can be multiplied by any arbitrary variable value, which is raised to 0. This nullifies the effect of the variable taken. 

Sample Questions

Question 1: Explain how the smallest natural number is a polynomial.

Answer:

Polynomials have variables depicted by whole number powers. The smallest natural number is 1, which is represented by the polynomial 1.x⁰, since any number raised to the power 0 is equivalent to 1. 

Question 2: Explain how the smallest whole number is a polynomial.

Answer:

Polynomials have variables depicted by whole number powers. The smallest whole number is 0, which is represented by the polynomial 0.x⁰, since any number raised to the power 0 is equivalent to 1. Also, any numeral or variable multiplied by 0 is equivalent to 0. 

Question 3: What type of polynomial is formed by the whole numbers?

Answer:

A monomial is formed by every whole number, since there is a single term in such a polynomial.

Question 4: What is the degree of a polynomial? What is the degree of such a polynomial formed by a whole number?

Answer:

The highest power to which any term in a polynomial is raised is called the degree of polynomial. The degree of the polynomial formed by a whole number is 0.

Question  5: Do whole number polynomials obey mathematical operations’ rules? 

Answer:

If we add two whole numbers, the resultant whole number is also a polynomial. Therefore, whole number polynomials obey mathematical operations’ rules.